The present invention relates generally to high performance systems and techniques for polishing workpieces. Specifically, the present invention relates to chemical mechanical polishing (CMP) apparatus and methods for improving the accuracy of conversion of data representing required CMP pressures to data representing CMP forces to be applied by a polishing (or planarization) head to a workpiece such as a semiconductor wafer, wherein quantization errors are minimized even though components having average resolution are used to provide some of the data used in the conversion operations.
In the fabrication of semiconductor devices, CMP operations are performed for buffing, cleaning, planarization, and polishing of wafers. A typical semiconductor wafer may be made from silicon and may be a disk that is 200 mm or 300 mm in diameter. The term xe2x80x9cwaferxe2x80x9d is used below to describe and include such semiconductor wafers and other planar structures, or substrates, that are used to support electrical or electronic circuits.
As integrated circuit device complexity increases, there is an increased need to improve the accuracy of CMP operations for planarizing dielectric materials deposited onto wafers. Also, as more metallization line patterns are formed in the dielectric materials, there is an increased need for higher accuracy in CMP operations that remove excess metallization.
In a typical CMP system, a wafer is mounted on a carrier with a surface of the wafer exposed. The carrier and the wafer rotate in a direction of rotation. The CMP process may be achieved, for example, when the exposed surfaces of the rotating wafer and of a polishing pad are urged into contact with each other by a polishing force, and when the wafer and the polishing pad move laterally relative to each other.
Two aspects of achieving accuracy of the polishing force applied to a wafer are of interest. Once a value of a required polishing pressure is specified, that value must first be accurately converted to a corresponding required force and then to a required force signal that accurately represents the required force. The force signal is applied to a force-producing device. Secondly, the actual force applied by the force-producing device must be measured and fed back to adjust the force signal. Improvements have been made to facilitate making repeatable measurements of the actual polishing forces applied to the wafer. However, there is still a need to more accurately convert the value of the required pressure to the value of the force signal. Such need exists, for example, in CMP systems in which the value of the required CMP force must be rapidly changed in relation to rapidly changing values of the exposed area of the wafer that is in contact with the polishing pad as the lateral position of the polishing pad changes relative to the wafer. CMP systems and methods in which the value of the required polishing forces are rapidly changed according to such rapidly changing values of the contact areas are described in co-pending U.S. patent application Ser. No. 09/748708, filed Dec. 22, 2000, entitled xe2x80x9cPOLISHING APPARATUS AND METHODS HAVING HIGH PROCESSING WORKLOAD FOR CONTROLLING POLISHING PRESSURE APPLIED BY POLISHING HEAD,xe2x80x9d by Miguel A. Saldana and Damon V. Williams (the Prior Application). Such Prior Application is hereby incorporated by reference.
The CMP systems and methods of the Prior Application implement a recipe (or set of instructions) for laterally moving the polishing pad relative to a wafer carrier and to a retaining ring on the carrier. The relative movement results in the rapidly changing values of the contact area between the polishing pad and the exposed surface of the wafer, and between the pad and a conditioning puck. Feedback of polishing pad position is coordinated with determinations of required values of the variable force by which such different contact areas are separately urged into contact with the polishing pad so that the pressure on each such different contact area may be controlled. The feedback is generated by an encoder that indicates the actual successive lateral positions of the polishing pad relative to the wafer, for example. The different value of each such separate contact area is determined based on the output of the encoder. For each respective pair of one such contact area and one such pressure to be applied to that contact area, a force signal is output (commanded) to represent a corresponding requested force. Each respective force signal is applied to the force-producing device (e.g., an actuator) which provides the force by which the one such contact area of the wafer, for example, is separately urged into contact with the polishing pad at the particular time at which the actual lateral position is measured.
Even though the invention of the Prior Application enables conversions of the value of the required pressure to the force signal, there is a need to increase the resolution of the commanded force signal when the actuator that is used displays analog controllability better than that of conventional digital control methods. For example, conventional pneumatic actuators have a low (or coarse) resolution, which provides steps or increments of 2.5 pounds of force. With such coarse resolution, the actuator may be used with the conventional digital control methods having a 10 bit resolution, for example. In detail, a range of polishing pressure may be 10 psi for a 200 mm wafer that has an area of about 50.26 square inches. The maximum force is 502.6 pounds (10 psixc3x9750.26 sq. in.). Force increments corresponding to the 10 bits are about 0.49 pounds (the force divided by the 1024 steps of the resolution). Thus, the increments of the mechanical resolution are more coarse than the 10 bit digital increments. However, when the actuator is a high resolution actuator capable of applying force in increments substantially less than 2.5 pounds (e.g., much less than the above exemplary 0.49 pounds), the conventional digital control methods do not provide the small increments of the commanded force signal that are necessary to take advantage of the high actuator resolution.
Another example illustrates errors that may result from use of devices having too low a resolution. Resolution is generally defined as 2 bit, 4 bit, n bit, etc. The number of output signals (or counts or steps) is 2 to the nth power. Thus, the very low 2 bit resolution corresponds to four counts or steps. In the context of the above-described required pressure, the resolution of the above-described digital methods dictates aspects of the force computation for converting the required pressure to the required force and to the value of the required force signal, and those aspects have an effect on accuracy. For example, the very low 2 bit resolution would correspond to a very low 2 bit computational resolution. Use of the 2 bit computational resolution would provide that a 10 psi pressure range be divided into four parts, such as discrete steps at 2.5 psi intervals, i.e., pressure values of 0, 2.5, 5.0, 7.5, and 10 psi. If the CMP system performs the conversion computations with respect to a required pressure having a value of 8.25 psi, for example, the increments (or steps) of the pressure may be 0.25 psi, which may be referred to as a parameter resolution increment. Also, 7.5 psi would be the value of the available output pressure step that is closest to the required 8.25 psi pressure. An accuracy problem resulting from such low resolution is shown by an example in which the required pressure value of 8.25 psi is to be input for processing. The conversion computation must convert the value of the required pressure (e.g., from psi to counts to voltage to counts and back to psi). Ideally, after the conversions, the required pressure would be output as exactly 8.25 psi. However, if the very low 2 bit resolution is used, the value of the required pressure would not exactly match the absolute value of any of the 0, 2.5, 5.0, 7.5, or 10 psi values of the steps of the pressure range. Use of the 7.5 psi value to represent the required 8.25 psi pressure would result in an error of 0.75 psi, or an error of 9.1 percent (9.1%) of the required 8.25 psi. Such a large error in current CMP systems would be unacceptable.
With this example in mind, the term xe2x80x9cquantizationxe2x80x9d is used herein to refer to a process of computation in which computational resolution is of significant importance in obtaining a computed result having an acceptable accuracy. A xe2x80x9cquantization processxe2x80x9d is quantization in which an initial value of a parameter is subjected to computational operations to obtain the computed result. Such exemplary 9.1% error resulting from the above exemplary quantization is referred to herein as a xe2x80x9cquantization errorxe2x80x9d. Generally, a high value of resolution results in steps having a small absolute value. With this in mind, in a normal situation, an unacceptable quantization error may result from performing the computation using too low a value of the computational resolution. For example, the above very low resolution may be the very low computational resolution (2 bits). A high absolute value (2.5 psi) of the steps of the computational resolution in such example was determined by dividing the count value of the very low 2 bit computational resolution (i.e., 4) into the 10 psi pressure range. Such high absolute value of the computational steps results in fewer steps. On the other hand, in the example the absolute value of the pressure (or parameter) increments (0.25 psi) is much less than the absolute value 2.5 psi. As noted above, the values of the exemplary 9.1% quantization error is unacceptable.
If a higher computational resolution were used, such as a 3 bit resolution, then the 10 psi pressure range would be divided by 8 (2 to the third power), and each step based on the higher resolution would have a smaller absolute value (1.25 psi). Use of the 1.25 psi absolute value steps would provide a computational step of 8.0 psi closest to the exemplary required 8.25 psi, and a quantization error of 0.25 psi, or 3.03 percent (3.03%) of the required 8.25 psi. This example shows that as the computational resolution increases, the number of steps increases, the value of each step decreases, and the quantization error decreases.
The method of determining the quantization error in each of the above-described examples is referred to as the xe2x80x9cnormal criteriaxe2x80x9d for determining whether an acceptable quantization error will result from the use of relatively low component resolution digital devices, such as digital to analog converters and analog to digital converters. Such normal criteria is not based on the principles of the present invention.
Continuing to use such digital devices as one example of a component having an availability that decreases as resolution increases, such digital devices are essential in determining the values of the command signals (voltages) applied to the actuators. However, there is limited availability of such digital devices having high component resolution (e.g., in excess of about 10 or 12 bits). Reference is made to the above-described need to increase the resolution of the commanded force signal when the actuator that is used displays analog controllability better than that of conventional digital control methods. Such need to increase component resolution is in conflict with the limited availability noted above. Therefore, as a basis for assuring availability of components, there is a need to use average resolution digital devices of 10 to 12 bits and at the same time increase the resolution of the commanded force signals. However, conventional ways of processing digital device output, and of performing the above conversions, for example, in the processing of the above-described pressure, area and force values, are in part based on use of the less available, high resolution digital devices, for example.
What is needed then, is a CMP system and method in which the accuracy of pressure and force command signals exceeds the resolution of mechanical actuating devices and which is less dependent on the use of high resolution, less available, components such as high resolution digital devices. In the required CMP system, such need is for a way to more accurately compute the value of forces to be applied to a wafer carrier, for example, as a polishing pad moves laterally relative to such wafer carrier during the CMP operation, wherein such computational accuracy does not depend on the use of high resolution digital devices. Moreover, such improved accuracy should be achieved even though the computation involves both digital and analog operations. Further, this improved computational accuracy should be achieved even though it may be necessary to convert values of required pressure or force, for example, from one set of units to a second set of units and then back to the first set of units. In such conversion, a value of a required pressure, for example, in the first set of units should have the same value after the conversion as before the conversion. In another sense, then, what is needed are methods and apparatus for quantization, which are effective without the use of high resolution digital devices, and in which the resulting average computational resolution is of less importance in obtaining computed results having an acceptable accuracy, such that quantization errors are eliminated or significantly reduced.
Broadly speaking, the present invention fills these needs by providing CMP systems and methods in which the accuracy of pressure and force computations is less dependent on the use of high resolution, less available components, such as high resolution digital devices such as digital to analog converters and analog to digital converters. The CMP system and methods of the present invention provide a way to more accurately compute the values of forces to be applied to a wafer carrier, for example, as a polishing pad moves laterally relative to such wafer carrier during the CMP operation. Such computational accuracy does not depend on the use of high resolution digital devices. Moreover, such improved accuracy is achieved even though the computation involves both digital and analog operations, and even though it may be necessary to convert values of required pressure or force, for example, from one set of units to a second set of units and then back to the first set of units. In such conversion, a pressure value, for example, in the first set of units may have the same value after the conversion as before the conversion. The present CMP system and methods enable a quantization process to be performed without the use of data from high resolution digital devices, and in which an average computational resolution is of less importance in obtaining computed results having an acceptable accuracy, such that quantization errors are eliminated or significantly reduced.
One aspect of the present invention relates to reducing quantization error in specifying CMP pressure in which a computational resolution is to be used in processing a required value of the pressure to obtain a computed value of the required pressure. Apparatus is provided for defining a relatively average value of the computational resolution (e.g., 10 to 12 bits), and for defining a set of values of pressure. The set contains possible values of the pressure, including the required value of the pressure. The highest value of pressure of the set is divided by the value of the computational resolution to obtain a series of pressure scales of the set. The pressure scales represent uniformly increasing possible values of the pressure, and the scales have equal ranges of pressure, each of which ranges has a value in excess of the value of the required pressure. A different first identifier is provided for each of the scales of the pressure, and the number of different first identifiers is equal to the value of the computational resolution. The required value of the pressure is specified by providing a different second identifier to indicate a set point value within any specific one of the scales. The set point corresponds to any particular pressure value. The number of different second identifiers is equal to the value of the computational resolution.
Another aspect of the present invention relates to a method of accurately representing, for computational processing, a required value among a pressure range of values of pressure to be applied to a wafer in chemical mechanical polishing. Operations of the method include dividing the pressure range by the value of a component resolution to define scale portions of the pressure range. Another operation generates a first output signal to identify one of the scale portions that includes the required value. A final operation generates a second output signal to identify a set point that defines the requested value in the identified scale portion.
Yet another aspect of the present invention relates to more accurately representing, for computational processing, a required value of a variable parameter, the value being among a range of parameter values. A system component, such as a digital device, is selected and has an operational resolution defined in terms of a number of increments. A computational signal range of a computational signal is defined to represent the amount by which the required values of the parameter may vary in the parameter range. A processor is programmed to divide the computational signal range by the number of increments of the operational resolution to represent a plurality of scales within the parameter range, each of the scales having a given number of units per increment, the number of scales being about equal to the number of increments. One of the scales is selected and includes a set point that identifies the required value of the parameter, the selected scale having a scale range of units. The selected scale is represented in terms of a first output signal that is within the computational signal range, and the set point is represented in terms of a second output signal that is within the computational signal range.
A further aspect of the present invention relates to reducing quantization error in a computation by defining synchronization data for synchronizing computational operations of first and second digital processors. The computational operations are performed on data representing a parameter. Based on the synchronization data, first and second data converting operations are performed by the first digital processor. The first data converting operation converts an initial value of the parameter to first digital data corresponding to one scale of a plurality of scales in a scale function. The one scale identifies one range of values of the parameter within an entire set of values of the parameter. The second data converting operation converts the initial value to second digital data corresponding to a range function that identifies one set point in the one range of values corresponding to the scale. Based on the synchronization data, the second digital processor converts the first and second digital data to a data item that digitally represents the exact initial value of the parameter.
An additional aspect of the present invention relates to reducing quantization error in a computation of CMP pressure. The synchronization data is defined for synchronizing operations of the first and second digital processors. The synchronization data defines a computational resolution, a set of values of the pressure to be used in computations, a set of values of output pressure data for communications between the first and second digital processors, a scale data conversion function that defines a relationship between a required polishing pressure and each one of a plurality of scales into which the set of values of the pressure is divided; and a set point data conversion function that defines a relationship between a range of the pressures in a particular one of the scales and a set point that defines one value of the required pressure in the particular scale. The first processor performs a first conversion operation based on the synchronization data. The first conversion operation is performed on a required value of the pressure, and converts the required value of the pressure to first output pressure digital data representing a particular one of the scales. The first digital processor also performs a second conversion operation based on the synchronization data. The second conversion operation is performed on the required value of the pressure to convert the required value to second output pressure digital data representing the set point that defines the required pressure in the particular scale. In the second processor a third conversion operation is performed based on the synchronization data. The third conversion operation is performed to convert the first output pressure digital data to scale data representing the particular one of the scales. A fourth conversion is performed by the second digital processor based on the synchronization data. The fourth conversion operation is performed on the second output pressure digital data to convert the second output pressure digital data to digital data more accurately representing the required value of the pressure.